3.46 PHOTONIC MATERIALS AND DEVICES
Lecture 10: LEDs and Optical Amplifiers
Notes
Lecture
References: B. Saleh, M. Teich, Photonics, (John-Wiley), Chapters 15-16. This lecture will review how electrons and holes recombine in semiconductors and generate photons. The study of light emission in materials is a key factor for the understanding of optoelectronic devices such
as LEDs, Optical Amplifiers and Lasers. Photon flux: φv = I
1
P 1
=
Eg
A Eg
I = optical power density
P = optical power
A = beam area
Non-equilibrium
R = non thermal generation rate (carrier injection rate) G0 = thermal generation rate n = n0 + Δn
p = p0 + Δp
Δn = Δp
Δn
n0 , p0
Injection carrier rate equation:
d(Δn)
Δn
= R−
dt
τ
τ = excess carrier recombination time (low injection level approximation) G0 = Bn0p0
G0 + R = Bnp
Δn − +
(e h pairs) / cm3 s
τ
= BΔn(n0 + p0 )
R=
τ≈
1
B (n0 + p0 )
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
Lecture 10: LEDs and Optical Amplifiers
Page 1 of 8
Lecture
Notes
Recombination: Non-equilibriumequilibrium
Recombination rate = B = Br + Bnr
Br = radiative
Bnr = non-radiative
Bnr ∝ σtraps v
Photon emission @ thermal equilibrium
GaAs
ni = 1.8 ×106 cm−3
Br = 10−10 cm3 / s
G0 = Br ni2 = 324
Photons
cm3 s
thickness of layer: t = 2 μm = 2 x 10-4 cm
( α ∼ 104 cm−1 )
φv = (Br ni2 ) t = 6.48 ×10−2 cm−2 s−1
Eg = 1.42 eV
= 2.27 ×10−19 J
I = φv Eg = 1.5 ×10−20 W/cm2
⇒
very low power
Internal Quantum Efficiency
Recombination = release of energy
radiating
→ hυ
non-radiating → hνphonon , Auger e
ηi =
Br
Br
=
B
Br + Bnr
ηi =
τnr
τ
=
τr
τr + τnr
: fraction of non-equilibrium
carriers that recombine radiatively
R·V = injected (pairs)/s
volume of active material
φ=
=
photon flux =
ηiRV
A
Δn
t
τr
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
Lecture 10: LEDs and Optical Amplifiers
Page 2 of 8
Lecture
Notes
Interband recombination
GaAs: ηi = 0.5
-5
Si:
ηi = 10
50 ns, ηi = 0.5, Δn = 1017 cm−3
GaAs : τ
R = Δn / τ = 1024 photons/cm3 / s
t = 2 μm
φv = Rt = 2 ×1020 cm−2 s−1
I = φvEg = 46 W/cm2
LED: 200 μm ×100 μm area
emitted power = 9 mW
Spontaneous emission
Rate = rsp (ν) =
1
ρ(ν )fe (ν )
τr
3
1
(2mr ) 2
ρ(ν )
=
(hν − Eg ) 2
2
π
optical joint density of states
1
1
1
=
+
mr
m v mc
(reduced mass)
Emission condition
fe (ν ) = fc (E2 )[1− fv (E1 )]
prob CB state
@ E1 empty
prob VB state
@ E2 filled
E1 = E2 − hν
mr
(hν − Eg )
mc
E 2 = Ec +
∞
φ=
V
rSP (ν )dν
A ∫0
3
=
V(mr )
A 2π
3
2
⎡ EFC −EFV − Eg ⎤
3
⎥
(k B Τ) 2 exp ⎢⎢
⎥
3
kBT
τr
⎣
⎦
2
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
Lecture 10: LEDs and Optical Amplifiers
Page 3 of 8
Notes
Lecture
(1) low injection ( Δn < n0
, p0 )
R ↑→ Δn ↑→ (EFC − EFV ) ↑
→ fe (ν ) ↑
(2) high injection ( Δn > n0 , p0 )
(EFC − EFV ) = Eg + (3π2 )
2
2
3
2mr
(Δn)
2
3
Spectral density of emission rate
⎡ −(hν −E )⎤
1
g ⎥
rsp = D(hν −Eg ) 2 exp ⎢⎢
⎥
KB T
⎢⎣
⎦
⎥
weak injection
3
⎡ (E −E −E )⎤
(2mr ) 2
FV
g ⎥
⎢ FC
D=
π 2 τr
exp ⎢
⎢⎣
kB T
⎥
⎥⎦
same shape as thermal equilibrium:
⎡ −(hν − E ) ⎤
1
g ⎥
rsp = D0 (hν − Eg ) 2 exp ⎢⎢
⎥
K
T
⎢⎣
B
⎦
⎥
Where
νP
⎡ (E −EFV ) ⎤
D
⎥
∼ exp ⎢⎢ FC
⎥
D0
k
T
B
⎣⎢
⎦⎥
= Peak frequency
1
hνP = Eg + k B T
2
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
λ g : bandgap wavelength
Eg : bandgap energy
λg =
1.24 eV ⋅ μm
Eg
Lecture 10: LEDs and Optical Amplifiers
Page 4 of 8
Lecture
Notes
FWHM
Δν = 1.8k B T / h
Hz (kBT in eV units)
2
P B
Δλ = 1.45λ k T μm
350Å
kBT(300K) = 0.025 eV
@ λ p = 1 μm
LED Devices
Internal photon flux
R=
I/ e
=
V
injection rate
I = current
e = charge/eV = active volume
@ high injection levels
Δn > n0 ,p0
Δn =
( I e) τ
t
V
Internal quantum efficiency
ηi ≡
A
photon flux
electron flux
C
I
φ = ηi A
e
B
Surface emission
External quantum efficiency
ηext =
external photon flux
electron flux
I
φout = ηext
A
e
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
Lecture 10: LEDs and Optical Amplifiers
Page 5 of 8
Lecture
1. Absorption (hν
η1 = exp (−αt)
Notes
Eg )
2. Reflection @ interface
2
(n − 1)
4n
η 2 = 1−
=
2
2
(n + 1) (n +1)
= 0.68 for GaAs
(n=3.6)
3. Total reflection
η3 = 1− cos θ c
1
2n2
= 4% of GaAs
ηext = η1 ⋅ η2 ⋅ η3
⋅ ηi
output power = P0 = h
νφ0
Pout = ηext
hν
I
e
Power conversion wall plug efficiency
emitted optical power
input electrical power
Pout
hν 1
=
= ηext
IV
e V
ηW ≡
voltage drop across device
Responsivity
P0
hν
= Vη W = ηext
I
e
1.24 W
R = ηext
λ 0 (μm) A
R≡
Typical:
ηext = 1.5% ⇒ R = 10-50 μW/mA
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
Lecture 10: LEDs and Optical Amplifiers
Page 6 of 8
Lecture
Notes
P0(μW) 2
1
0
0
100
200 Luminous performance (displays)
I(mA)
P ⋅ eye sensitivity
lumens
= 0
IV
IV
ηext (%)
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
Lecture 10: LEDs and Optical Amplifiers Page 7 of 8 p-type
2a
2b
2c
2d
2. Typical LED device and chip configurations. (a) Crosssection of a LED lamp. The LED chip, typically 250 x 250 x 250
micrometers, is mounted in a reflecting cup formed in lead frame.
Clear epoxy acts as a lens, as well as performing other functions.
(b) A conventional homojunction LED chip can be made with
GaAsP:N/GaP structures to emit at red and yellow wavelengths,
and with GaP:N/GaP structures to emit at green wavelengths.
(c) In a red-emitting AlGaAs double-heterostructure chip, the
entire structure is grown by LPE and can be either n-type or ptype on top. (d) An AllnGaP double-heterostructure with a GaP
window layer for red, yellow, or green emitters. The Al
concentration in the p-type active region is adjusted to give the
desired color.
3.46 Photonic Materials and Devices
Prof. Lionel C. Kimerling
Lecture 10: LEDs and Optical Amplifiers
Page 8 of 8